Properties

Label 5915.2.a.bp
Level $5915$
Weight $2$
Character orbit 5915.a
Self dual yes
Analytic conductor $47.232$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5915,2,Mod(1,5915)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5915, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5915.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5915 = 5 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5915.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(47.2315127956\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 21 q + 4 q^{2} + 5 q^{3} + 20 q^{4} + 21 q^{5} + 4 q^{6} + 21 q^{7} + 9 q^{8} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 21 q + 4 q^{2} + 5 q^{3} + 20 q^{4} + 21 q^{5} + 4 q^{6} + 21 q^{7} + 9 q^{8} + 28 q^{9} + 4 q^{10} + 2 q^{11} + 23 q^{12} + 4 q^{14} + 5 q^{15} + 18 q^{16} - 6 q^{17} + 32 q^{18} + 8 q^{19} + 20 q^{20} + 5 q^{21} - 17 q^{22} - 14 q^{23} + 27 q^{24} + 21 q^{25} + 11 q^{27} + 20 q^{28} + 20 q^{29} + 4 q^{30} + 22 q^{31} + 22 q^{32} + 33 q^{33} + 22 q^{34} + 21 q^{35} - 8 q^{36} + 48 q^{37} + 42 q^{38} + 9 q^{40} - 5 q^{41} + 4 q^{42} - 27 q^{43} - 4 q^{44} + 28 q^{45} + 9 q^{46} + 27 q^{48} + 21 q^{49} + 4 q^{50} - 4 q^{51} - 28 q^{53} + 27 q^{54} + 2 q^{55} + 9 q^{56} + 56 q^{57} + 44 q^{58} + 7 q^{59} + 23 q^{60} + 25 q^{61} - 17 q^{62} + 28 q^{63} + 47 q^{64} - 30 q^{66} + 40 q^{67} - 19 q^{68} + 13 q^{69} + 4 q^{70} + 15 q^{71} + 42 q^{72} + 16 q^{73} + 37 q^{74} + 5 q^{75} + 58 q^{76} + 2 q^{77} - 10 q^{79} + 18 q^{80} + 25 q^{81} + 14 q^{82} - 11 q^{83} + 23 q^{84} - 6 q^{85} + 35 q^{86} + 65 q^{87} - 74 q^{88} + 24 q^{89} + 32 q^{90} - 89 q^{92} + 82 q^{93} + 21 q^{94} + 8 q^{95} - 22 q^{96} + 57 q^{97} + 4 q^{98} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.54595 0.867067 4.48187 1.00000 −2.20751 1.00000 −6.31871 −2.24819 −2.54595
1.2 −2.53402 0.274221 4.42125 1.00000 −0.694882 1.00000 −6.13550 −2.92480 −2.53402
1.3 −2.06819 0.524302 2.27742 1.00000 −1.08436 1.00000 −0.573763 −2.72511 −2.06819
1.4 −1.76432 −2.79517 1.11284 1.00000 4.93158 1.00000 1.56524 4.81295 −1.76432
1.5 −1.42081 3.33012 0.0187087 1.00000 −4.73148 1.00000 2.81504 8.08969 −1.42081
1.6 −1.32241 2.15086 −0.251224 1.00000 −2.84433 1.00000 2.97705 1.62621 −1.32241
1.7 −1.05806 −1.50254 −0.880506 1.00000 1.58978 1.00000 3.04775 −0.742381 −1.05806
1.8 −0.872229 −1.78534 −1.23922 1.00000 1.55722 1.00000 2.82534 0.187428 −0.872229
1.9 −0.381801 2.01941 −1.85423 1.00000 −0.771013 1.00000 1.47155 1.07803 −0.381801
1.10 −0.136571 0.775570 −1.98135 1.00000 −0.105921 1.00000 0.543737 −2.39849 −0.136571
1.11 0.449582 −0.613470 −1.79788 1.00000 −0.275805 1.00000 −1.70746 −2.62366 0.449582
1.12 0.826316 −3.03579 −1.31720 1.00000 −2.50852 1.00000 −2.74106 6.21602 0.826316
1.13 0.952302 −2.74726 −1.09312 1.00000 −2.61623 1.00000 −2.94559 4.54746 0.952302
1.14 1.06682 3.07881 −0.861896 1.00000 3.28453 1.00000 −3.05313 6.47906 1.06682
1.15 1.37365 1.75471 −0.113079 1.00000 2.41036 1.00000 −2.90264 0.0789971 1.37365
1.16 1.55527 −1.25293 0.418865 1.00000 −1.94865 1.00000 −2.45909 −1.43016 1.55527
1.17 2.01969 −2.51514 2.07915 1.00000 −5.07981 1.00000 0.159865 3.32594 2.01969
1.18 2.03843 2.35682 2.15519 1.00000 4.80422 1.00000 0.316346 2.55462 2.03843
1.19 2.52854 3.10549 4.39352 1.00000 7.85236 1.00000 6.05211 6.64408 2.52854
1.20 2.54977 1.71797 4.50132 1.00000 4.38043 1.00000 6.37779 −0.0485752 2.54977
See all 21 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.21
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(7\) \(-1\)
\(13\) \(-1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5915.2.a.bp yes 21
13.b even 2 1 5915.2.a.bo 21
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5915.2.a.bo 21 13.b even 2 1
5915.2.a.bp yes 21 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5915))\):

\( T_{2}^{21} - 4 T_{2}^{20} - 23 T_{2}^{19} + 105 T_{2}^{18} + 200 T_{2}^{17} - 1137 T_{2}^{16} - 755 T_{2}^{15} + 6612 T_{2}^{14} + 525 T_{2}^{13} - 22578 T_{2}^{12} + 5415 T_{2}^{11} + 46557 T_{2}^{10} - 19744 T_{2}^{9} - 57394 T_{2}^{8} + \cdots - 125 \) Copy content Toggle raw display
\( T_{3}^{21} - 5 T_{3}^{20} - 33 T_{3}^{19} + 193 T_{3}^{18} + 397 T_{3}^{17} - 3073 T_{3}^{16} - 1722 T_{3}^{15} + 26077 T_{3}^{14} - 4484 T_{3}^{13} - 127331 T_{3}^{12} + 76017 T_{3}^{11} + 361154 T_{3}^{10} - 314954 T_{3}^{9} + \cdots + 8128 \) Copy content Toggle raw display